Method for confident registration-based non-uniformity correction using spatio-temporal update mask

ABSTRACT

A scene-based non-uniformity correction method to achieve a fixed-pattern noise reduction and eliminate ghosting artifacts based on robust parameter updates via a confident inter-frame registration and spatio-temporally consistent correction coefficients. The method includes the steps of: Assessing an input image frame whether the input image frame has a sufficient scene detail for registrations to prevent false registrations originated from low-detail scenes, calculating horizontal and vertical translations between frames to find a shift, introducing a scene-adaptive registration quality metric to eliminate erroneous parameter updates resulting from unreliable registrations and applying a Gaussian mixture model (GMM)-based temporal consistency restriction to mask out unstable updates in non-uniformity correction parameters.

CROSS REFERENCE TO THE RELATED APPLICATION

This application is the national stage entry of InternationalApplication No. PCT/TR2018/050194, filed on Apr. 27, 2018, the entirecontents of which are incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to a scene-based non-uniformitycorrection method to achieve better fixed-pattern noise reduction andeliminate ghosting artifacts based on robust parameter updates viaconfident inter-frame registration and spatio-temporally consistentcorrection coefficients.

BACKGROUND

Infrared imagery has been used in various fields such as military,medical, surveillance and numerous industrial branches. One of the mainproblems with commonly used focal plane arrays (FPA) is the fixedpattern noise (FPN) formed by the non-uniform response of detectorelements [1]. As a solution to this problem, there are two mainapproaches, namely, calibration based and scene based non-uniformitycorrection (NUC) methods. Calibration based methods [1-4] traditionallyuse reference uniform surfaces to correct non-uniform detectorresponses. These methods are preferred due to their simplicity andcomputational efficiencies. However, they are not very convenient duringoperational use, since they require additional equipment and interruptthe video flow. On the other hand, the family of scene based methods[5-13] deal with non-uniformity problem using only scene content, whichalleviates the operational problems of calibration based methods.Because of these benefits, there are considerable amount of studiesutilizing scene based approaches.

One of the early works uses neural network (NN) structure to updatecalibration coefficients [5] without any consideration of scene content.Naturally, this approach will suffer from ghosting artifacts due to theassumption that all pixel elements will have a similar temporal averagewhich does not always hold. There are other constant-statisticsassumption based methods that further improve on this work [6]. However,they have similar drawbacks that result in ghosting artifacts. Some ofthe recent studies [13-15] employ inter-frame registration to matchscene content which notably decreases the ghosting artifacts. Despitethe success of [15] in reducing the artifacts, moving objects in thescene, motion blur and registration errors still remain as a problem. In[13], Zeng et al. made further improvement by introducing a spatialupdate mask from residual registration errors. This mask is used toselectively update the correction coefficients in order to reduceghosting artifacts. Although this work significantly limits theartifacts, there are several issues that might still stand as problems.One problem is that there might be a global registration errorespecially in low-detail frames. The method applies certain restrictionsonly within the error image between frames and does not examine whetherthe registration is performed correctly. In mis-registration cases,severe ghosting artifacts may occur. Additionally, there is no mechanismto prevent temporally inconsistent updates possibly caused byregistration errors.

SUMMARY

The proposed invention offers a method for confident registration-basednon-uniformity correction using spatio-temporal update mask. Theconfident registrations are achieved by introducing a scene adaptiveregistration quality metric to discard erroneous updates. A Gaussianmixture model (GMM)-based spatio-temporal update mask is utilized toselectively refine the estimations of correction coefficients. Theresults of experiments on an extensive dataset consisting of bothsynthetically corrupted data and real infrared videos show that theproposed algorithm achieves superior performance in PSNR (PeakSignal-to-Noise Ratio) and roughness metrics with notably lower ghostingartifacts when compared to other state-of-the-art methods.

Our contribution is two-fold. The first one is that we eliminateerroneous parameter updates resulting from unreliable registrations. Thesecond one is that we employ a temporal consistency restriction on thecorrection coefficients to further eliminate unstable parameter updates.

In our method, we aim to address the remaining ghosting artifactproblems by introducing a scene-adaptive registration quality metric toachieve a confident registration before updating any non-uniformityparameter estimation. We first assess the input image frame whether itis eligible for registration in terms of sufficient scene detail. Thisprevents false registrations originated from low-detail scenes. Then werequire a certain amount of translation to ensure a sufficientstatistical variation. After those restrictions, we then assure thatthere is no considerably large global registration error utilizing theintroduced scene-adaptive registration quality metric. Theserestrictions could cause to discard too many useful frames, however, byintroducing an adaptive frame delay mechanism, we provide a way toefficiently wait for a good candidate frame with sufficient translationand acceptable registration errors. Finally, for any remaining errorsthat might produce artifacts, we utilize a GMM-based temporalconsistency restriction that masks out statistically unstable updates innon-uniformity correction parameters.

In conclusion, the present invention introduces a new scene-based NUCmethod that yields better performance by making more accurate FPNestimates and by eliminating ghosting artifacts utilizingspatio-temporally consistent FPN estimation update mechanisms. Inessence, the proposed algorithm tries to eliminate erroneous FPNestimates by the assessment of registration errors, amount of shiftbetween images and temporal consistency of FPN characteristics. Theresults of the experimentations show that a better performance in FPNcorrection without ghosting artifacts is achieved in an extensivedataset.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of the present invention.

FIG. 2 shows PNSR performance of the evaluated methods. The titles ofthe plots represent the image sequence names as given in the originalETH-ASL Thermal Image Dataset [17].

FIG. 3 shows ghosting artifacts comparison among the evaluated methodsexecuted on a dataset.

FIG. 4 shows ghosting artifacts visible in the error images that belongsto the frames shown in FIG. 3.

FIG. 5 shows comparison of ghosting artifacts among the evaluatedmethods executed on the ETH-ASL dataset [17].

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention relates to a confident image registration basednon-uniformity correction algorithm that utilizes a spatio-temporalupdate mask. A block diagram demonstrating the flow of the algorithm isgiven in FIG. 1.

1. Observation Model

In order to model the response of infrared detector pixels, the commonlinear model approach is utilized [1]. According to this model, theobserved output signal is represented by a linear function of trueresponse as given in (1):y _(n)(i,j)=x _(n)(i,j)·a _(n)(i,j)+b _(n)(i,j)  (1)where x_(n) is the true response for the n^(th) frame, y_(n) is theassociated detector output signal, (i, j) is the pixel coordinates and aand b are the gain and offset coefficients.

Based on this model, true response can also be written as a linearfunction of the detector output as shown in (2):x _(n)(i,j)=y _(n)(i,j)·g _(n)(i,j)+o _(n)(i,j)  (2)where backward gain g_(n)(i,j) is equal to 1/a_(n)(i,j) and backwardoffset o_(n)(i,j) is equal to −b_(n)(i,j)/a_(n)(i,j).

According to this model, the observed signal is corrected by using thebackward gain and offset coefficients. These coefficients can beestimated using different techniques. In the proposed method,inter-frame registration is performed with adaptive frame delay andleast mean squares (LMS) minimization is used for estimating the gainand offset coefficients.

2. Registration

In frame registration based non-uniformity correction approaches, themain assumption is that the different pixels must produce the sameresponse to the same scene data. Since the fixed pattern noise is aslowly varying signal, this assumption can be used for estimating thecorrection coefficients iteratively using LMS minimization [8]. For thispurpose, the first step is to find the correct registration between theframes.

Linear model parameters are initialized by setting gain values to 1 andoffset values to 0. After obtaining the corrected signals x_(n) andx_(n−m), the horizontal shift δ_(xn) and the vertical shift δ_(yn)between these signals are calculated. In the registration block, theimage detail magnitude Φ_(n) and the registration quality value ξ_(n)are calculated for ignoring the problematic registrations caused byvarious reasons such as lack of scene details, motion blur and camerarotation. In other words, the correction parameters are updated onlywhen a confident registration is achieved. This selective updateapproach is an important process for eliminating ghosting artifacts.Details of each sub-block are given in the following subsections.

2.1. Scene Detail Calculation

In order to achieve a reliable registration, sufficient scene detailmust be present. Otherwise, matching can be erroneous due to lowsignal-to-noise ratio. Therefore, the registration and the otherparameter update steps are skipped to ensure a robust registrationquality, if the newly arrived frame does not contain sufficient scenedetail (Φ_(n)<T_(Φ)).

For a given frame, scene detail magnitude φ_(n) is calculated as givenin (3):

$\begin{matrix}{\phi_{n} = {\frac{1}{WH}\left( {{{x_{n}*h}}_{2}^{2} + {{x_{n}*h^{T}}}_{2}^{2}} \right)}} & (3)\end{matrix}$where W is frame width, H is frame height, h is horizontal edge filterkernel and * is discrete convolution operation. In our implementation,9×9 extension of horizontal Sobel kernel is used as the edge filter.2.2. Inter-Frame Shift Calculation

Instead of using 1-D projections of intensity values for shiftcalculation as in [13], we employ 1-D projections of edge image whichprovides more robust registration performance in scenes with rich edgecontent. Since the edge image is already calculated in (3) for detailcalculation, we efficiently obtain the 1-D projections in vertical andhorizontal directions as shown in (4):

$\begin{matrix}{{{P_{n}^{x}(j)} = {\sum\limits_{i = 1}^{W}{E_{n}\left( {i,j} \right)}}},{{P_{n}^{y}(i)} = {\sum\limits_{j = 1}^{H}{E_{n}\left( {i,j} \right)}}}} & (4)\end{matrix}$where E_(n) represents the edge image calculated as shown in (5):

$\begin{matrix}{{E_{n}\left( {i,j} \right)} = {\left( {\sum\limits_{k = {- r}}^{r}\;{\sum\limits_{l = {- r}}^{r}{{x_{n}\left( {{i - k},{j - l}} \right)}{h\left( {k,l} \right)}}}} \right)^{2} + \;\left( {\sum\limits_{k = {- r}}^{r}\;{\sum\limits_{l = {- r}}^{r}{{x_{n}\left( {{i - k},{j - l}} \right)}{h^{T}\left( {k,l} \right)}}}} \right)^{2}}} & (5)\end{matrix}$where h is the edge filter of size r×r used in Scene Detail Calculation.

In order to calculate the shift between the current and delayed images,normalized cross correlation of the projection vectors are calculated asshown in (6):

$\begin{matrix}{{{\gamma_{x}(i)}\overset{\Delta}{=}{\sum\limits_{x}\;\frac{\left( {{P_{n - m}^{y}\left( {i + x} \right)} - \overset{\_}{P_{n - m}^{y}}} \right)\left( {{P_{n}^{y}(x)} - \overset{\_}{P_{n}^{y}}} \right)}{{\sigma p}_{n}^{y}{\sigma p}_{n - m}^{y}}}}{{\gamma_{y}(j)}\overset{\Delta}{=}{\sum\limits_{y}\;\frac{\left( {{P_{n - m}^{x}\left( {j + y} \right)} - \overset{\_}{P_{n - m}^{x}}} \right)\left( {{P_{n}^{x}(y)} - \overset{\_}{P_{n}^{x}}} \right)}{{\sigma p}_{n}^{x}{\sigma p}_{n - m}^{x}}}}} & (6)\end{matrix}$where P_(n) ^(x) and P_(n) ^(y) are the means and σP_(n) ^(x) and σP_(n)^(y) are the standard deviations of the projection vectors P_(n) ^(x)(j)and P_(n) ^(y)(i), respectively. Similar definitions apply for theprojection vectors for the delayed frame as well.

Shift in x and y directions are than retrieved as shown in (7):

$\begin{matrix}{{\delta_{x} = {\underset{i}{{{argmax}\gamma}_{x}}(i)}}{\delta_{y} = {\underset{j}{{{argmax}\gamma}_{y}}(j)}}} & (7)\end{matrix}$2.3. Registration Quality Assessment

One of the major sources of the erroneous model updates is theregistration errors that stem from the violation of pure translationassumption. To overcome such problems, we utilize a registration qualitymeasure that discards the frame pairs which have relatively large globalregistration error compared to scene detail magnitude. In other words,we introduce an adaptive metric that shows relative registration qualitywith respect to scene detail magnitude. The registration quality measureis defined as shown in (8):

$\begin{matrix}{\psi_{n} = \frac{\phi_{n}}{\left. {\frac{1}{WH}\sum\limits_{i,j}} \middle| {{E_{n}\left( {i,j} \right)} - {E_{n - 1}\left( {{i + \delta_{x}},{j + \delta_{y}}} \right)}} \right|}} & (8)\end{matrix}$

This metric favors the registrations where the error magnitude is asmall fraction of scene detail magnitude. Registrations with lowerquality measure than a certain threshold T_(v) are discarded at theparameter update step.

3. Non-Uniformity Correction Model Update

In general, the observation model discussed above is updated as theminimization of the LMS problem stated in [5] as given in (9):a _(n+1)(p,q)=a _(n)(p,q)−η₁ ·e _(n)(p,q)·y _(n)(p,q)·ξ_(st) _(n) (p,q)b _(n+1)(p,q)=b _(n)(p,q)−η₂ ·e _(n)(p,q)·ξ_(st) _(n) (p,q)  (9)where, subscripts n and n+1 represents the current and next frameindices, (p, q) represents the index range within the registered overlapregion between the delayed and current image, η₁ and η₂ are the learnrates for the gain and offset updates, e_(n) is the error image betweenthe corrected current frame and the delayed frame, y_(n) is the currentinput frame and ξ_(st) _(n) is the spatio-temporal update mask whichdetermines pixel locations at which the observation model will beupdated.

It is noted that there is a 2-pass update for the model which exploitsthe fact that the registered overlapping regions of the delayed andcurrent frames coincide with different pixel locations of the FPA. Thus,it is possible to update the gain and offset coefficients for two pixellocations instead of one by repeating the update step in bothdirections.

The calculation of the error map e_(n) and spatio-temporal update maskξ_(st) _(n) will be detailed in further sections.

3.1. Error Map Calculation

The error map yields the error between the intensities read fromdifferent FPA pixel locations for the same scene content assuming theregistration error is sufficiently small. This information provides thedifference between the FPA element responses at different locations. Theerror calculation is performed on the corrected signals as given in(10):e _(n)(i,j)=x _(n−m)(i+δ _(x) ,j+δ _(y))−x _(n)(i,j)  (10)3.2. Spatial Mask for Model Update

Although the generated error maps in 3.1 to find non-uniform responses,unfortunately, not all error values are valid due to residualregistration errors, moving objects in the scene and so forth. As an apriori information, non-uniformity characteristics for each pixel in anFPA does not vary radically; unless they are defective [16]. Based onthis, erroneous updates can be further avoided in addition to theelimination of global registration errors explained in Section 2.3. Thisis achieved by masking out the outlier error values on the previouslycalculated error map as given in (11):

$\begin{matrix}{{\xi_{s_{n}}\left( {p,q} \right)} = \left\{ \begin{matrix}1 & \left. {\left. {{if}\mspace{14mu}\left( {{e_{n}\left( {p,q} \right)} - \mu_{e_{n}}} \right)} \right) < \left( {c\sigma}_{e_{n}} \right)} \right) \\0 & {otherwise}\end{matrix} \right.} & (11)\end{matrix}$where, c is the constant for σ distance which determines the outlierthreshold. μ_(e) _(n) and σ_(e) _(n) are the mean and standard deviationof the error map, respectively.3.3. GMM-Based Temporal Mask for Model Update

Up to this point, we have generated an update mask that avoids globalregistration errors and spatially inconsistent non-uniformity errors. Asa final precaution for erroneous model parameter updates, we exploit thefact that FPN has an approximately constant behavior over time [7].Thus, any update that would yield radically different model parametersis considered invalid and masked out from calculations. Analogous to thebackground subtraction domain, we could model residual FPN in theregistration error map as fixed background and model other temporallyinconsistent errors as the foreground. As a commonly applied solution tobackground subtraction problem, GMM could be successfully used to detectand eliminate the error components that do not belong to FPN. The GMMupdate steps are given in the following equations:

$\begin{matrix}{{\Delta\left( {i,j} \right)} = {{e_{n}\left( {i,j} \right)} - {\mu_{{GMM}_{n}}\left( {i,j} \right)}}} & (12) \\{{\xi_{{st}_{n}}\left( {i,j} \right)} = \left\{ \begin{matrix}{\xi_{s_{n}}\left( {i,j} \right)} & {{{if}\mspace{14mu}{\Delta\left( {i,j} \right)}^{2}} < {{\lambda\sigma}_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \\0 & {otherwise}\end{matrix} \right.} & (13) \\{{\mu_{{GMM}_{n + 1}}\left( {i,j} \right)} = {{\mu_{{GMM}_{n}}\left( {i,j} \right)} + {\alpha_{1}{\Delta\left( {i,j} \right)}} + {\xi_{{st}_{n}}\left( {i,j} \right)}}} & (14) \\\begin{matrix}{{var}_{{GMM}_{n + 1}} = {\sigma_{{GMM}_{n + 1}}^{2}\left( {i,j} \right)}} \\{= {\sigma_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \\{{+ {\alpha_{2}\left\lbrack {{\Delta\left( {i,j} \right)}^{2} - {\sigma_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \right\rbrack}}{\xi_{{st}_{n}}\left( {i,j} \right)}}\end{matrix} & (15)\end{matrix}$where ξ_(st) _(n) represents the spatio-temporal update mask computedusing GMM model. μ_(GMM) and σ² _(GMM) are the mean image and varianceimage kept by the GMM. They are initialized by using the spatiallymasked regions (ξ_(s) _(n) ) of the first input image frame. Also, λ isthe temporal variance threshold coefficient, α₁ is the update learn ratefor the GMM mean image and α₂ is the learn rate for the GMM varianceimage.4. Adaptive Frame Delay

In order to obtain a robust registration between the frames, a minimummagnitude of inter-frame shift and scene detail is required. If theseconditions do not hold for the incoming frames, we drop them and waitfor a better candidate for the parameter update. In other words, delaybetween two registration frames is not necessarily one, but can takevalues between one and m_(max). When the maximum frame delay m_(max) isreached before finding a suitable image frame, the process restarts withnew initial frame.

5. Process Steps of the Invention

The observation model for the fixed pattern noise on infrared (IR) imageis considered to be consisting of a multiplicative gain terms andadditive offset terms. If these terms are found then the fixed patternnoise is estimated and can be corrected from the noisy image to obtainan uncorrupted clean image. In the following steps, our aim is to findthese correction terms.

After the IR image is captured by a sensing device, the algorithms firststarts a registration process between image frames. The first step ofthis process is to check whether the frames to be registered containsufficient detail information. This step is necessary to avoid erroneousregistrations caused by insufficient detail in the images. It is checkedby applying a Sobel filter to extract the average magnitude of edgeinformation in the images. Then this information is compared with asuitable threshold. If the scene detail is lower than the threshold, thealgorithms do not proceed to registration steps. This way, registrationperformance is improved by avoiding the potentially erroneousregistrations.

The images with sufficient scene detail are then used to find a shiftbetween the frames. For the registration, the 1-D horizontal was usedand vertical projections of the edge maps generated from the originalframes using edge extraction filter. Then the 1-D projection vectors arematched using cross-correlation. This way, horizontal and verticaltranslations between the frames are calculated.

Even after the scene detail assessment, the registration performance maystill not be as good as desired. Hence, a registration quality metric isdefined to quantify the registration performance. This metric is foundby calculating the ratio of average registration error and the averagescene detail magnitude. Average registration error is simply the framedifference between the edge maps of the frames and scene detailmagnitude is readily calculated. This ratio is expected to be small forgood registration, hence, a threshold is used for this metric anddiscontinue registration process if this metric is smaller than thedesignated threshold. This step helps to reduce errors caused by poorregistration performance.

After these steps, two sufficiently well registered image frames areobtained. These frames provide same image region measured from differentsensor pixels within the registered overlap region. Using the assumptionthat same regions should produce same responses in the imaging pixels,non-uniformity errors can be found. Using these errors, gain and offsetcorrection terms can be updated. Due to the fact that fixed patternnoise does not change at a fast rate, the updates with a slow learningrate is made to avoid premature convergence. Also, not all the pixelsare updated at once. There are spatial and temporal consistency masks todetermine which pixel locations are to be updated. The use of both thespatial and temporal constraints provides robustness to thenon-uniformity correction terms updates. This is a novel approach toreduce the ghosting artifacts produced by erroneous estimations of thecorrection terms.

In order to update non-uniformity correction terms, the error mapbetween sensor element responses in the overlap regions of two shiftedframes is found. The error map is simply the difference of the overlapregions of the two frames.

In the fact that typical behavior of fixed pattern noise does not changeradically between pixels in an IR image sensor. Hence, it can be deducedthat error values that are too different from its neighboring pixels areprobably caused by erroneous calculations. These errors are mostlycaused by scene changes that violate the translation assumption such asmotion blur, non-rigid scene motion and so forth. Therefore, the pixelsthat have error map values deviating from its local neighborhood with acertain amount is marked. The marked pixels are considered spatiallyinconsistent and hence the correction terms for the corresponding pixelsare not updated.

Another characteristic of the fixed pattern noise is that it has anapproximately constant behavior over limited time durations. Using thisinformation, the temporal variation of the error map values isconstrained. If temporal variation is higher that a factor of variancethreshold, it can be considered that error map values are not valid andcorrection terms for such pixel locations are not updated. This isachieved by the use of Gaussian Mixture Models. Analogous to backgroundsubtraction case, consistent error map values are considered asbackground and temporally changing error map values are considered asmoving foreground. Then, the deviations of error map values from thetemporal mean value estimations are found. These deviations are comparedagainst the thresholds which are a factor of temporal varianceestimations. The pixels with higher temporal error map deviations aremasked out and the correction terms at these locations are not updated.The temporal mean and variance estimations are also updated at thenon-masked pixel locations for iteratively improving the GMM mean andvariance estimations similar to the update mechanism of non-uniformitycorrection terms.

When any of the conditions detailed in abovementioned steps, then thecurrent couple of frames are not valid to find correction term updates.In such cases, one could drop both frames and wait for another couple ofconsecutive frames which would satisfy the constraints. However, thismay not always be necessary. If the first frame has sufficient scenedetail but registration performance is not satisfactory, then we cankeep the first frame and wait only for another second frame until amaximum number of trials is reached. This way, one not only try toregister the consecutive frames, but also the frames with more than oneframe delay. This adaptive frame delay strategy for registration ensuresnot to unnecessarily drop frames and provides faster convergence for theestimation of non-uniformity correction terms.

6. Experiments

The proposed method is compared against the state-of-the-art scene-basedNUC methods: GE-NUC [13], IRLMS [15] and GLMS [8]. The evaluation iscarried out with an extensive dataset containing synthetically corruptedclean IR images from a public dataset (ETH-ASL Thermal Image Dataset[17]) and uncorrected IR images with FPN captured with various IRdetectors. The performance comparison is conducted using the objectivemetrics described in the following section.

6.1. Performance Metrics

The experiments are performed on both images with synthetically addednoise and real noisy thermal images. For synthetically corrupted images,Peak Signal-to-Noise Ratio (PSNR) metric is used which measures theerror between the expected (clean) reference image and the imagecorrected by the scene based NUC methods. PSNR calculation is given in(16):PSNR=10 log₁₀(peakval²/MSE)  (16)where, MSE is the mean-squared-error between the output and targetimages and peakval is the maximum value that the input signal can take.

For the real fixed pattern noise case, however, PSNR metric cannot becalculated, since the clean reference images are not available. In theliterature, roughness metric which measures the high frequency componentof the image is commonly used [13]. Roughness metric ρ is calculated asgiven in (17):

$\begin{matrix}{\rho = \frac{\left. ||{\hat{X}*h}||{}_{2}{+ \left. ||{\hat{X}*h^{\prime}} \right.||_{2}} \right.}{\left. ||\hat{X} \right.||_{2}}} & (17)\end{matrix}$

where, {circumflex over (X)} is the corrected image frame, h=[−0.5, 0.5]is the horizontal high-pass filter kernel and h^(l) is the verticalversion of the kernel.

6.2. Dataset

In a scene-based NUC study, the dataset variety is vital in terms ofboth the scene content and different detector responses. In theexperiments, our objective is to prevent over-fitting to some limiteddata and observe the behavior of the methods in possible failurescenarios. Thus, we would like to observe the effects of scene contents,camera motion, detector characteristics and noise characteristics.

We used two different datasets in our experiments. The first dataset isETH-ASL Thermal Image Dataset [17] which is publicly available [18].This dataset has a rich scene content involving people, animals,buildings, cars, terrain, sky, etc. The images are recorded using a FLIRTau 320 camera with a resolution of 324×256 and bit-depth of 16-bits.The clean images in this dataset is corrupted by a synthetic Gaussiannoise of μ=0 and σ=10. In order for the synthetic FPN to be morerealistic, the amount of noise is gradually increased from 60% to 100%of the full scale. There are 7 sequences having a total of 3409 framesin the selected dataset.

The second dataset is a collection of images recorded using ASELSANthermal imagers with a resolution of 640×512 and bit-depth of 16-bits.There are both hand-held and pan-tilt camera images in the datasetcontaining a variety of scenes such as terrain, sky, buildings, trees,people and so forth. In total, there are 5 sequences having 3785 frames.The image sequences have real uncorrected FPN so that the methods areevaluated in physical world conditions.

6.3. Results

The experimentation results are assessed both objectively by comparingthe PSNR and roughness measurements and subjectively by observing thecorrection performances and ghosting artifacts.

In FIG. 2, PSNR plots of each method are given for all frames of eachdata sequence in ETH-ASL [17] dataset. The main reason for a detailedplot is that the performance loss caused by the ghosting artifacts orfalse FPN estimations in the middle sections of the image sequenceswould not be observable by inspecting only the average PSNR values forthe whole sequence. Another benefit of these plots is that theconvergence of the methods are easily visible. It is noted that theproposed method produces the best PSNR results in all sequences for allframes after its late convergence. The strategy of the proposed methodis clearly imprinted on the PSNR characteristics. Our method assessesall the conditions such as registration quality, frame shift amount,scene detail magnitude and temporal consistency. If all the requirementsare matched, only then a noise estimation update is performed.

This strategy provides more accurate estimations at the expense of fewerestimation updates. The stability of the estimations of our algorithm isalso reflected on the PSNR curve showing no oscillation unlike thecompared methods. For a brief summary, average PSNR values for eachsequence and overall average for the whole dataset are given in Table 1.

TABLE 1 PSNR Performance Comparison (dB) GLMS IRLMS GE-NUC CORESUMSempach6 −16.86 −13.32 −13.14 −12.33 Sempach7 −16.93 −12.82 −12.91−11.17 Sempach8 −16.87 −14.48 −11.81 −10.51 Sempach9 −16.84 −12.32−12.22  −9.72 Sempach10 −16.64 −12.47 −12.41 −10.38 Sempach11 −17.02−16.59 −12.87 −10.67 Selnpach12 −18.41 −15.77 −11.96 −11.84 Average−17.22 −13.99 −12.37 −11.08

Due to the fact that the roughness metric is highly scene-dependent, thevalues are usually close and characteristics of the methods are somewhatsimilar. The proposed method again produces the best (lowest) roughnessvalues in overall performance for each data sequence. This result isgiven in the average roughness values given in Table 2.

TABLE 2 Roughness Performance Comparison (ρ) GLMS IRLMS GE-NUC CORESUM(×10⁻³) (×10⁻³) (×10⁻³) (×10⁻³) Seq01  4.809  4.801  4.798  4.651 Seq02 4.292  4.115  3.984  3.883 Seq03  3.171  2.887  2.927  2.883 Seq0414.318 13.159 12.977 11.994 Seq05  1.453  1.276  1.205  1.130

In the scene-based NUC domain, ghosting artifacts are the arch enemiesof the algorithms. One of the main contributions of our method is theelimination of such artifacts, thus, it is useful to view some exemplarycases for the evaluated methods. FIG. 3 depicts the ghosting artifactsproduced by the compared methods. Although quite visible in the outputimages of the algorithms, it is easier to note the ghosting artifacts inthe error correction images (difference of output image and originalimage) in FIG. 4. For other images, the artifacts are burnt into thecorrections while no such artifacts are observed for our method.

Similar ghosting artifacts could be seen in the ETH-ASL public dataset[17] results given in FIG. 5. Again, it is noted that our method doesnot yield any noticeable ghosting artifact whereas others do atdifferent scales.

REFERENCES

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What is claimed is:
 1. A method for a scene-based non-uniformitycorrection to achieve a fixed-pattern noise reduction and eliminateghosting artifacts in an infrared imagery, comprising the steps of:assessing an input infrared image frame for scene detail forregistrations to prevent false registrations that originated fromlow-detail scenes, calculating horizontal and vertical translationsbetween the input infrared image frames to find a shift, introducing ascene-adaptive registration quality metric to eliminate erroneousparameter updates resulting from unreliable registrations, applying aGaussian mixture model (GMM)-based temporal consistency restriction tomask out unstable updates in non-uniformity correction parameters;wherein the horizontal and vertical translations between the inputinfrared image frames are calculated by using 1-D horizontal andvertical projections of edge maps generated from original input infraredimage frames using an edge extraction filter and matching 1-D projectionvectors using a cross-correlation; wherein the 1-D horizontal andvertical projections are calculated with the equations:${{P_{n}^{x}(j)} = {\sum\limits_{i = 1}^{W}\;{E_{n}\left( {i,j} \right)}}},{{{P_{n}^{y}(j)} = {\sum\limits_{j = 1}^{H}\;{E_{n}\left( {i,j} \right)}}};}$wherein p_(n) ^(x)(j) is the horizontal projection vector and P_(n)^(y)(i) is the vertical projection vector; where E_(n) represents anedge image calculated as:${{{{E_{n}\left( {i,j} \right)} = \left( {\sum\limits_{k = {- r}}^{r}\;{\sum\limits_{l = {- r}}^{r}{{x_{n}\left( {{i - k},{j - l}} \right)}{h\left( {k,l} \right)}}}} \right)^{2}};} + \;\left( {\sum\limits_{k = {- r}}^{r}\;{\sum\limits_{l = {- r}}^{r}{{x_{n}\left( {{i - k},{j - l}} \right)}{h^{T}\left( {k,l} \right)}}}} \right)^{2}};$where x_(n) is the true response for the n^(th) input infrared imageframe and h is an edge filter of size r×r used in a scene detailcalculation.
 2. The method according to claim 1, wherein a sufficiencyof scene detail is checked by applying a Sobel kernel as an edge filterto extract an average magnitude of edge information in the inputinfrared image frames and comparing the edge information with athreshold.
 3. The method according to claim 1, wherein a shift betweencurrent and delayed images in x and y directions are calculated withequations: ${\delta_{x} = {\underset{i}{{{argmax}\gamma}_{x}}(i)}};$${\delta_{y} = {\underset{j}{{{argmax}\gamma}_{y}}(j)}};$ where anormalized cross correlation of the 1-D projection vectors arecalculated as:${{\gamma_{x}(i)}\overset{\Delta}{=}{\sum\limits_{x}\;\frac{\left( {{P_{n - m}^{y}\left( {i + x} \right)} - \overset{\_}{P_{n - m}^{y}}} \right)\left( {{P_{n}^{y}(x)} - \overset{\_}{P_{n}^{y}}} \right)}{{\sigma p}_{n}^{y}{\sigma p}_{n - m}^{y}}}};$${{\gamma_{j}(j)}\overset{\Delta}{=}{\sum\limits_{y}\;\frac{\left( {{P_{n - m}^{x}\left( {i + x} \right)} - \overset{\_}{P_{n - m}^{y}}} \right)\left( {{P_{n}^{y}(x)} - \overset{\_}{P_{n}^{y}}} \right)}{{\sigma p}_{n}^{x}{\sigma p}_{n - m}^{x}}}};$where P_(n) ^(x) and P_(n) ^(y) are means and σP_(n) ^(x) and σP_(n)^(y) are standard deviations of the 1-D projection vectors P_(n) ^(x)(j)and P_(n) ^(y)(i), respectively.
 4. The method according to claim 1,wherein an error calculation is performed on the corrected signals as:e _(n)(i,j)=x _(n−m)(i+δ _(x) ,j+δ _(y))−x _(n)(i,j); wherein x_(n) is atrue response for an n^(th) frame, and δ_(x) and δ_(y) are a shiftbetween current and delayed images in x and y directions and arecalculated with equations:${\delta_{x} = {\arg\;{\max\limits_{i}{\gamma_{x}(i)}}}};$$\delta_{y} = {\arg\;{\max\limits_{j}{{\gamma_{y}(j)}.}}}$
 5. The methodaccording to claim 4, comprising the step of masking out outlier errorvalues on a calculated error map to avoid erroneous updates in additionto an elimination of global registration errors by using the equation:${\xi_{s_{n}}\left( {p,q} \right)} = \left\{ {\begin{matrix}1 & \left. {\left. {{if}\mspace{14mu}\left( {{e_{n}\left( {p,q} \right)} - \mu_{e_{n}}} \right)} \right) < \left( {c\sigma}_{e_{n}} \right)} \right) \\0 & {otherwise}\end{matrix};} \right.$ where, c is a constant for σ distance, whereinthe constant for the σ distance determines an outlier threshold, μ_(e)_(n) and are a mean and a standard deviation of an error map,respectively.
 6. A method for a scene-based non-uniformity correction toachieve a fixed-pattern noise reduction and eliminate ghosting artifactsin an infrared imagery, comprising the steps of: assessing an inputinfrared image frame for scene detail for registrations to prevent falseregistrations that originated from low-detail scenes; calculatinghorizontal and vertical translations between the input infrared imageframes to find a shift; introducing a scene-adaptive registrationquality metric to eliminate erroneous parameter updates resulting fromunreliable registrations; applying a Gaussian mixture model (GMM)-basedtemporal consistency restriction to mask out unstable updates innon-uniformity correction parameters; wherein an observation model for afixed pattern noise on the input infrared image frames is:y _(n)(i,j)=x _(n)(i,j)·a _(n)(i,j)+b _(n)(i,j); wherein the fixedpattern noise on the input infrared image frames consists ofmultiplicative gain terms and additive offset terms to be found forestimating and correcting the fixed pattern noise to obtain anuncorrupted clean image, where x_(n) is a true response for an n^(th)frame, y_(n) is an associated detector output signal, (i, j) is pixelcoordinates and a and b are gain and offset coefficients; furthercomprising the steps of: performing an inter-frame registration with anadaptive frame delay and using a least mean squares (LMS) minimizationfor estimating the gain and offset coefficients; and updating theobservation model as a minimization of the LMS problem:a _(n+1)(p,q)=a _(n)(p,q)−η₁ ·e _(n)(p,q)·y _(n)(p,q)·ξ_(st) _(n) (p,q);b _(n+1)(p,q)=b _(n)(p,q)−η₂ ·e _(n)(p,q)·ξ_(st) _(n) (p,q); whereinsubscripts n and n+1 represents current and next frame indices, (p, q)represents an index range within a registered overlap region between adelayed image and a current image, η₁ and η₂ are learn rates for gainand offset updates, e_(n) is an error image between a corrected currentframe and a delayed frame, y_(n) is a current input frame and ξ_(st)_(n) is a spatio-temporal update mask, wherein the spatio-temporalupdate mask determines pixel locations, wherein the observation model isconfigured to be updated at the pixel locations.
 7. The method accordingto claim 6, wherein a GMM-based update is applied by using equations:$\begin{matrix}{{{\Delta\left( {i,j} \right)} = {{e_{n}\left( {i,j} \right)} - {\mu_{{GMM}_{n}}\left( {i,j} \right)}}};} \\{{\xi_{{st}_{n}}\left( {i,j} \right)} = \left\{ {\begin{matrix}{\xi_{s_{n}}\left( {i,j} \right)} & {{{if}\mspace{14mu}{\Delta\left( {i,j} \right)}^{2}} < {{\lambda\sigma}_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \\0 & {otherwise}\end{matrix};} \right.} \\{{{\mu_{{GMM}_{n + 1}}\left( {i,j} \right)} = {{\mu_{{GMM}_{n}}\left( {i,j} \right)} + {\alpha_{1}{\Delta\left( {i,j} \right)}} + {\xi_{{st}_{n}}\left( {i,j} \right)}}};} \\\begin{matrix}{{var}_{{GMM}_{n + 1}} = {\sigma_{{GMM}_{n + 1}}^{2}\left( {i,j} \right)}} \\{= {\sigma_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \\{{{+ {\alpha_{2}\left\lbrack {{\Delta\left( {i,j} \right)}^{2} - {\sigma_{{GMM}_{n}}^{2}\left( {i,j} \right)}} \right\rbrack}}{\xi_{{st}_{n}}\left( {i,j} \right)}};}\end{matrix}\end{matrix}$ where ξ_(st) _(n) represents the spatio-temporal updatemask computed using a GMM model, μ_(GMM) and σ² _(GMM) are a mean imageand a variance image kept by the GMM, ξ_(s) _(n) states spatially maskedregions of a first input infrared image frame, λ is a temporal variancethreshold coefficient, α₁ is an update learn rate for the mean imagekept by the GMM and α₂ is the update learn rate for the variance imagekept by the GMM.
 8. A method for a scene-based non-uniformity correctionto achieve a fixed-pattern noise reduction and eliminate ghostingartifacts in an infrared imagery, comprising the steps of: assessing aninput infrared image frame for scene detail for registrations to preventfalse registrations that originated from low-detail scenes; calculatinghorizontal and vertical translations between the input infrared imageframes to find a shift; introducing a scene-adaptive registrationquality metric to eliminate erroneous parameter updates resulting fromunreliable registrations; applying a Gaussian mixture model (GMM)-basedtemporal consistency restriction to mask out unstable updates innon-uniformity correction parameters; wherein a scene detail magnitude,Φ_(n), is calculated:${\phi_{n} = {\frac{1}{WH}\left( \left. ||{x_{n}*h}\mathop{\text{||}}_{2}^{2}{+ \left. ||{x_{n}*h^{T}}||_{2}^{2} \right.} \right. \right)}};$where W is a frame width, H is a frame height, where x_(n) is a trueresponse for an n^(th) frame, h is a horizontal edge filter kernel and *is a discrete convolution operation.
 9. The method according to claim 8,wherein an adaptive metric showing a relative registration quality withrespect to scene detail magnitudes is defined as:${\psi_{n} = \frac{\phi_{n}}{\left. {\frac{1}{WH}\sum\limits_{i,j}} \middle| {{E_{n}\left( {i,j} \right)} - {E_{n - 1}\left( {{i + \delta_{x}},{j + \delta_{y}}} \right)}} \right|}};$and the registrations with a lower quality measure than a certainthreshold are discarded at a parameter update step; wherein E_(n)represents an edge image calculated as: $\begin{matrix}{{{E_{n}\left( {i,j} \right)} = \left( \;{\sum\limits_{k = {- r}}^{r}{\sum\limits_{l = {- r}}^{r}\;{{x_{n}\left( {{i - k},{j - l}} \right)}{h\left( {k,l} \right)}}}} \right)^{2}};} \\{{+ \left( \;{\sum\limits_{k = {- r}}^{r}{\sum\limits_{l = {- r}}^{r}{{x_{n}\left( {{i - k},{j - l}} \right)}{h^{T}\left( {k,l} \right)}}}} \right)^{2}};}\end{matrix}$ wherein h is an edge filter of size r×r used in a scenedetail calculation.